The so-called mathematical model of control system is a mathematical expression describing the relationship between input, output and internal variables of the system. The differential equation of control system is a time-domain mathematical model to describe the system performance. However, when the system changes, it is not convenient to rewrite and solve the differential equation. In engineering, Laplace transform is needed to solve the differential equation and establish the relationship between output and input, that is, the transfer function is the mathematical model of the system in S domain.

1. Establish a mathematical model by using the laws of kinematics.

Force balance equation and motion law equation are the basis of variable kinematics analysis. The listed higher-order differential equations are often difficult to solve, so the transfer function is obtained by Laplace transform, and then the stability or performance index is analyzed. Therefore, the establishment of mathematical model is more critical.

2. Establish a mathematical model by using circuit theory.

The law of current or voltage in the circuit reflects its parameters, and its performance is studied according to the control theory.

3. Establish the dynamic structure diagram and find the transfer function.

Dynamic structure diagram is another algorithm for finding transfer function, which is very flexible in practical work.